Question

В школе учится менее 500 детей. Известно, что в шести классах поровну учеников и в общей сложности более 150 человек, а в оставшихся классах в общей сложности на 15% больше школьников, чем в этих шести классах. Сколько учеников в этой школе?​

Answer 1

Ответ:

всего учеников  387

Пошаговое объяснение:

Интересная задачка.

Пусть в каждом из 6 классов по n учеников (естественно n∈N).

Тогда в 6 классах всего 6n учеников. По условию эти 6n>150.

В оставшихся классах всего 6n*1.15 (по условию на 15% больше).

Всего в школе 6n+1.15*6n учеников            (*)

6n+1.15*6n<500 (по условию).

6n(1+1.15)<500; ⇒ 6n*2.15<500;       n<500/(2.15*6); ⇒ n<38 (ведь n∈N)

6n>150;                  n>150/6;          ⇒ n>25;                     n>25.

Итак:

25<n<38

Возможных вариантов всего 12:

26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37

возьмем каждое число, и умножим его на 6 и на 2,15 (см. формулу (*))

"На выходе" ищем натуральное число. Это число  единственное: 387 для n=30!

Проверяем:

в 6 классах 30*6=180 >150;

всего учеников 180*2,15= 387 <500

в "остаьных" классах 387-180=207 учеников

разница между классами 207/180=1,15.

Вот так примерно.

Answer 2

Calculation of the Number of Students in the School

To calculate the number of students in the school, we need to analyze the given information. Let's break it down step by step:

1. In six classes, there are an equal number of students, and the total number of students in these six classes is more than 150. 2. In the remaining classes, the total number of students is 15% more than the total number of students in the six classes.

Let's assume the number of students in each of the six classes is x.

According to the first statement, the total number of students in these six classes is more than 150.

According to the second statement, the total number of students in the remaining classes is 15% more than the total number of students in the six classes.

To calculate the number of students in the school, we need to find the value of x and then calculate the total number of students.

Let's solve the problem step by step:

1. The total number of students in the six classes is more than 150. Let's assume it is y.

2. The total number of students in the remaining classes is 15% more than the total number of students in the six classes. This can be calculated as:

Total number of students in remaining classes = y + (15/100) * y

3. The total number of students in the school is the sum of the students in the six classes and the students in the remaining classes:

Total number of students in the school = y + (15/100) * y + y

Now, let's solve the equations to find the value of y and then calculate the total number of students in the school.

Calculation Steps:

1. Let's assume the number of students in each of the six classes is x. 2. The total number of students in the six classes is more than 150, so we can write the equation as: 6x > 150 3. Simplifying the equation, we get: x > 25 4. The total number of students in the remaining classes is 15% more than the total number of students in the six classes, so we can write the equation as: (15/100) * 6x = (15/100) * y 5. Simplifying the equation, we get: 0.9x = (15/100) * y 6. The total number of students in the school is the sum of the students in the six classes and the students in the remaining classes, so we can write the equation as: Total number of students = 6x + (15/100) * y + y 7. Substituting the value of x from equation 3, we get: Total number of students > 6 * 25 + (15/100) * y + y Total number of students > 150 + (15/100) * y + y 8. Simplifying the equation, we get: Total number of students > 150 + (15/100 + 1) * y Total number of students > 150 + (115/100) * y 9. Since the total number of students is an integer, we can assume that y is a multiple of 100. Let's assume y = 100. 10. Substituting the value of y in equation 8, we get: Total number of students > 150 + (115/100) * 100 Total number of students > 150 + 115 Total number of students > 265

Therefore, the total number of students in the school is greater than 265.

Please note that the exact number of students in the school cannot be determined based on the given information. We can only conclude that the total number of students is greater than 265.